MathAlgebraLinear algebraMatrix decomposition

Spectral decomposition

The steps of the decomposition

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Order the steps to construct a spectral decomposition of any symmetric matrix $A=U D U^T$ .

Put the items in the correct order

Find all the eigenvalues of

A

Build

U

with the elements all the orthonormal bases.

Form an orthonormal basis for every eigenspace.

Compute the eigenspace of every eigenvalue.

Build

D

with the eigenvalues

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